Singular limit of a two-phase flow problem in porous medium as the air viscosity tends to zero

TL;DR

This paper investigates the behavior of a two-phase flow in porous media as the air viscosity approaches zero, demonstrating convergence to solutions of a generalized Richards model.

Contribution

It provides a rigorous proof of the convergence of solutions in the singular limit of zero air viscosity, linking two-phase flow to the Richards model.

Findings

Convergence of subsequences to generalized Richards solutions

Validation of the singular limit as air viscosity tends to zero

Mathematical foundation for simplified models in porous media flow

Abstract

In this paper we consider a two-phase flow problem in porous media and study its singular limit as the viscosity of the air tends to zero; more precisely, we prove the convergence of subsequences to solutions of a generalized Richards model.